THE HECKE OPERATORS ON S(K)(GAMMA(1)(N))

In this paper we describe the space of the cusp forms with the weight k for the congruence subgroup GAMMA 1(N), S(k) (GAMMA 1 (N)), using Eichler-Shimura isomorphism, Shapiro lemma and the theory of group cohomology. An algorithm computing an integral basis of S(k) (GAMMA 1 (N)) is developed. Applying the Hecke operators on the basis we can determine newforms in S(k) (GAMMA 1 (N)).